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Lie quasi-states
classification
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math.SG
keywords
algebrafunctionalslinearquasi-statessymplecticabelianasymptoticcontinuous
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Lie quasi-states on a real Lie algebra are functionals which are linear on any abelian subalgebra. We show that on the symplectic Lie algebra of rank at least 3 there is only one continuous non-linear Lie quasi-state (up to a scalar factor, modulo linear functionals). It is related to the asymptotic Maslov index of paths of symplectic matrices.
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